Voltage divider



Sept. 27, 1960 w. A. MENZEL 2,954,517 VOLTAGE DIVIDER Filed Jan. 8, 19532 Sheets-Sheet 2 2L I i I ZNVENTOR 0 V V2 l WOLFGANG A. MENZEL ATTORNEYSUnited States Patent VOLTAGE DIVIDER Wolfgang A. Menzel, Silver Spring,Md., assignor to the United States of America as represented by theSecretary of the Navy Filed Jan. 8, 1953, Ser. No. 330,366

Claims. (Cl. 323-74) (Granted under Title 35, US. 'Code (1952), sec.266) The invention described herein may be manufactured and used by orfor the government of the United States of America for governmentalpurposes without the payment of any royalties thereon or therefor.

This invention relates to a voltage divider and more particularly to apotentiometer designed to produce two voltages having a ratio varyingaccording to an exponential function.

For many purposes in electrical circuits the voltage change is desiredto be exponential. For example, an analysis of the electric stabilizedtime fuze circuit shows that a linear time setting requires anexponential change in the ratio of two voltages. Heretofore, this hasbeen accomplished by dividing a multiple turns potentiometer into equalsegments and by inserting suitable parallel resistances converting thedivider to the desired exponential ratio. This structure is delicate andexpensive and does not provide suflicient accuracy.

The presently disclosed voltage divider provides a means for obtainingan exponential ratio between two voltages by combining a plurality ofnormally linear potentiometers. It consists of four potentiometersarranged on a single axis and having the contact arms connected in sucha manner as to give two output voltages, the ratio of which follows theexponential'function with an accuracy of one part in two million forrange e x varying from 0 to 1.

An object of the present invention is to provide a voltage divider whichproduces an exponential ratio between the resulting voltages.

A further object of this invention is to provide a voltage divideremploying four linear potentiometers of such values that the resultingvoltages vary according to an exponential ratio.

Other objects and many of the attendant advantages of this inventionwill be readily appreciated as the same 0 becomes better understood byreference to the following detailed description when considered inconnection with the accompanying drawings wherein:

Fig. 1 shows one form of a voltage divider constructed according to thepresent invention;

Fig. 2 illustrates another species of this invention;

Fig. 3 shows the preferred embodiment of a voltage divider; and

Fig. 4 is a graph showing the variation of 3 from e where x varies from0 to 1 by employing the voltage divider of Fig. 3.

Referring now to the drawings and more specifically to Fig. 1 it can beseen that there is provided a voltage divider having ganged wipercontacts, or sliders 1 and 2. Output voltages E and E, are obtainedacross wiper contact 1 and the common output, or reference, point 12,and across wiper contact 2 and reference point 12, respectively. Thereare provided resistances R R and R disice posed in series as shown andacross which is impressed a voltage E which can be supplied by anysuitable source, such as battery 13. When x=0 the sliders are in theupper position and when x=1 the sliders are in the lower position. E isaccepted as a fixed voltage as shown in Fig. 1. Accordingly when x: 1, E=E and and x=l. The accuracy of the ratio l +1 E 'E.B,.

will be calculated for the case in which E and E vary through one halfthe total range of e". By definition of the exponential function in E,E0 E, 13

From this equation E is found equal to The values of A and B may beevaluated when 4:1 as A=E E and Substituting the derived value of E intothe original equation the final equation for the voltage divider shownin Fig. 1 becomes:

E 1 +xh Z 1] E3 lW x e From this equation the ratio of may be calculatedfor various values of x yielding the following results:

Table I 1 [1 X T: Ratio E meets the theoretical values for x=0, x=1 and.-==.5. The maximum error is dx=.004. With XII/7', this means a maximumtiming error of 120 milliseconds for 'r=30 seconds. In other words atime fuze for 30 seconds maximum time has no error due to the voltagedivider at settings of 0, 15, 30 seconds, but the deviation is +120milliseconds at 7.5 seconds and -120 milliseconds at 22.5 seconds.Whilethis accuracy is suflicient for many purposes, it is not adequatefor fuze application.

. In Fig. 1, E is accepted as a constant. However, it can be shown thatE varies between when x =0 and when x=1. The deviation of E from alinear function between these values is slight and therefore a linearpotentiometer may be provided to vary E as E; and E are varied. Such avoltage divider is shown in Fig. 2. There The voltage divider of Fig. 1yields the general equation to meet the curve e at three points. If x=0,.5 and l are the meeting points then a and b can be calculated and theresulting equation gives coincidence at these points. In order toimprove the accuracy of the voltage divider it would be necessary toincrease the number of points ofcoincidence thereby increasing the orderof the rational function by which is expressed. This gives the equationI 1+a x+ b x E3 1 llg$+ 17 50 In this case the coefficients a [7 a bmust be determined to give coincidence points with the curve e Assumingthese points to be at x=0, .25, .5, .75 and 1 then:

a =.5411S855 b =.10755897 a =.45871O32 b =.06523960 Comparing with ewith the above calculated coefficients gave values shown in thefollowing table:

I II are provided sliders 4, 5 and 6 which are ganged as shown. Tab e ISlider 5 serves the function of impressing at point 7 a varying voltagecorresponding to a linear variation of E 5 A Ratio E M1016 X E Theoutput voltages E and B are obtained across wiper 3 arm 4 and referencepoint 12, and across wiper arm 6 [1] [2] and reference point 12,respectively. This voltage divider may beexpressed by the followingequation: 0.0 1.000000000 1.000000000 1.000000000 0.0000

0.1 1. 105170018 1.105105522 1. 000004882 +4. 882 m 1] 0.2 1 2214027581221400527 1.000001820 +1.826 [1:z;] [1-:c]+a; 0.3 1 3408588081.349860571 0. 000008003 l.307 El-erl 101803 301880 200080 .1053 E3 +'E0Z0 1:82211880O 1:5322115631 11000001730 +11 730 -1 e 0.7 2. 0137527072013750077 1. 000001300 +1300 08 2.225540028 2225545003 0000008108-1.332 e 0. 0 2. 450003111 2. 450015131 0. 000005113 -4. 887 1+z[-[-2]+x 1- 1.0 2. 718281828 2. 718281828 1.000000000 0.000

2e 1 e 1x[2 +0 1- for or by the general equation El 1 5 2 l-i-Ax-l-Cx E31 (1 16+ 17210 2 1 a =().54115855 b =0.1075589 This equation yields thefollowing results: =0 45 871()32 b =0.06523960 Table 11 ,It is apparentthat the voltage divider of Fig. 1 must El [1] be modified to include apotentiometer arrangement vary- X '5 Ratiom i140 ing proportional to mxThe voltage divider of Fig. 3 provides such an arrangement. There areprovided [11 I21 00 sliders 8 9 10 and 11 which are I 1 ganged as shown.In thi od' lta E E are oh- 000 1.000000000 1.000000000 1.0000000000.0000 t Z the outgut 2 gas 1 altld t 3 t 0.1 1.105170018 1.1051400201000022523 +0.2252 ame acmss P all common P P0111 100003 130080 1330201200 andwipwm2800330323230212,383- 014 l:491824698 1140155004211000184141 +11 8414 lively; Sliders 10 With 'lesistofs 5 alld 4 gg%.ggg'figg l pggtgggggg wgggg igg ig-g spectively are added to yield thesquare function hereggwgwgg g? .lIIbGfOl'fi I'BfGITEd t0. voltagedlVldfil' gives the 01- 55 00 5 2 0.0 2. 450003111 2, 450523370 1.000032417 +0. 324 lpwmg who for 1.0 2. 718281828 2. 71828182 1.000000000+0. 0000 1 E2 for R R e 1 2. 0 [21+ 8 [121111212 E V :0 e1 :0 E3 2M 3R1+ R3 xR1+x $10 R The coefiicients of this equation must equal themethcients a b a b previously calculated. However, all resistance valuescan be expressed in terms of the single resistor R; as follows: Withthere is:

Since r and r;, are close to 1, for simplification purposes R may beassumed equal to R and R;,. A voltage divider with R =R =R gives goodaccuracy with an error of not more than .0043 percent.

This invention with the foregoing calculations demonstrates that acombination of five linear resistance units, four of which arepotentiometers assembled on one axis can produce output voltages havinga ratio which follows the exponential function with an accuracy of onepart in two million for the range e [x:0 1].

Obviously many modifications and variations of the present invention arepossible in the light of the above teachings. It is therefore to beunderstood that within the scope of the appended claims the inventionmay be practiced otherwise than as specifically described.

What is claimed as new and desired to be secured by Letters Patent is:

1. An electrical circuit comprising a potential energy source, aplurality of series connected linear resistance elements connectedacross said source, a common output terminal defined in the electricalcircuit, and ganged wiper contacts individually coupled to two of saidresistance elements, the instantaneous potentials appearing across eachof said ganged contacts and said common output terminal as said contactsare moved across their respective resistance elements exhibiting anexponential relationship therebetween.

2. An electrical circuit comprising a potential energy source, aplurality of series connected linear resistance elements connectedacross said source, a common output terminal defined in the electricalcircuit, ganged wiper contacts individually coupled to two adjoiningresistance elements of said plurality of resistance elements, theeffective resistance between said adjoining resistance elements beingselectively varied by said contacts being electrically isolated fromeach other, the movement of said ganged wiper contact in a manner toprovide instantaneous output potentials between each of said gangedcontacts and said common terminal exhibiting an exponential relationshiptherebetween.

3. An electrical circuit comprising a potential energy source, a bankhaving a plurality of serially connected linear resistance elementsconnected across said source, a common output terminal defined by onejuncture between said source and said bank, a first movable outputterminal electrically coupled to one of said elements for developing avariable output potential between said first and said common outputterminals correlative to the movement of said first terminal on said oneelement, a second movable output terminal electrically coupled to theresistance element adjoining said one element for developing a variableoutput potential between said second and said common output terminalscorrelative to the movement of said second terminal on said adjoiningelement, said movable output terminals being ganged for movement inunison on their respective resistance elements in a manner toselectively vary the effective resistance between the adjoining elementsto effect an exponential relationship between said output potentials.

4. An electrical circuit comprising a potential energy source, a firstbank of a plurality of serially connected linear resistance elementsconnected across said source, a second bank of a plurality of seriallyconnected linear resistance elements connected across said source, acommon output terminal defined by one juncture between said first bankand said source, a first movable output terminal electrically coupled toone of the elements in said first bank for developing a variable outputpotential between said first and said common terminals correlative tothe movement of said first terminal on said one element, a secondmovable output terminal electrically coupled to the element adjoiningsaid one element in said first bank for developing a variable outputpotential between said second and said common terminals correlative tothe movement of said second terminal on said adjoining element, amovable contact electrically coupled to one of the elements in saidsecond bank and to the juncture between said one and adjoining elementson said first bank, said movable contact and terminals being ganged formovement in unison on their respective elements to effect an exponentialrelationship between said output potentials.

5. An electrical circuit comprising a potential energy source, a bank ofinterconnected linear resistance elements coupled across said source,said bank including a plurality of serially connected elements and oneelement connected in parallel with one of said serially connectedelements, a movable contact electrically coupled to the one seriallyconnected element and to said parallel connected element, a firstmovable output terminal electrically coupled to one of said plurality ofserially connected elements for developing a variable output potentialbetween said first terminal and a common terminal correlative to themovement of said first terminal on the one element, a second movableoutput terminal electrically coupled to the element adjoining said oneof said serially connected elements for developing a variable outputpotential between said second terminal and a common terminal correlativeto the movement of said second terminal on said adjoining element, amovable common terminal electrically coupled to said parallel connectedelement, said movable contact and terminals being ganged for movement inunison on their respective elements to effect an exponentialrelationship between said output terminals.

References Cited in the file of this patent UNITED STATES PATENTS1,858,364 Koenig May 17, 1932 2,417,442 Parkinson Mar. 18, 19472,448,885 Hooven Sept. 7, 1948 2,453,462 Sellers Nov. 9, 1948 2,573,280Schmidt Oct. 30, 1951 FOREIGN PATENTS 698,560 Germany Nov. 13, 1940

